The aim of this continuing project is the development and evaluation of improved statistical methods for the analysis of case-control data. The case-control study is a primary tool for epidemiological research into the relationship between 'exposure' variables or other risk factors and disease incidence. The methods under development promise more precise and comprehensive evaluation of the effect of such exposure variables and may lead to liberalization of case-control study design. The main focus of this project is the adaptation of prospective disease incidence models to case-control sampling. Models considered include the proportional hazards regression model, in which exposure and other factors are presumed to affect the (instantaneous) disease incidence rate in multiplicative manner, and the associated logistic regression model in which such factors affect the odds-ratio multiplicatively. We have developed a conditional likelihood procedure for adapting the proportional hazards model to 'time-stratified' case-control data. Numerical aspects and estimation properties based on this likelihood will be studied under this proposal. A central aim of the proposal is the adaptation of the same model in a form that utilizes the whole time-exposure history of individual study subjects and need not require time-stratified sampling. In addition we expect to complete, under this proposal, ongoing work showing the duality of representation and estimation from prospective and retrospective logistic models. Some non-iterative methods for logistic estimation will also be further studied.